Argument by assertion is the logical fallacy where someone tries to argue a point by merely asserting that it is true, regardless of contradiction. While this may seem stupid, it's actually an easy trap to fall into and is quite common.

This is not the same as establishing initial axioms on which to build a framework of logic or ideas.

It is also well known as rhetoric, because an assertion itself isn't really a proof of anything, or even a real argument - assertion only demonstrates that the person making the statement believes in it. An inability to provide anything other than an argument by assertion may be the result of brainwashing, basing ones belief on blind faith or ignorance as to what forms a proper argument. Those who argue by assertion often do think that they're making a real argument. They might simply not realise where they haven't provided a full argument. The point of constructive debate or discourse is to draw attention to this sort of thing, and for people to further develop and evolve their arguments in response. A truly fallacious argument by assertion is when someone continues to assert without advancing their argument, even after it has been pointed out.

A repeated argument by assertion can also take the form of non sequitur that requires little effort to make and is therefore often used to fatigue people who make actual arguments — sometimes combined with the infamous Gish Gallop. They will then bow out of the debate, usually exhausted, having lost faith in humanity and muttering, "How the hell do you reason with these people?!?!" through grinding teeth — at which point the individual making the assertive argument simply declares victory.

It is important to note that this is not the same as the presenter being unable to lay out the all the reasoning, due to constraints. Math and science classes are great examples. Important results — say, Fubini's theorem in calculus — cannot always be proven on the spot.